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Simplifying log(x + 1) + -1log(7 + -1x) = -1log(2) Reorder the terms: glo(1 + x) + -1log(7 + -1x) = -1log(2) (1 * glo + x * glo) + -1log(7 + -1x) = -1log(2) (1glo + glox) + -1log(7 + -1x) = -1log(2) 1glo + glox + (7 * -1glo + -1x * -1glo) = -1log(2) 1glo + glox + (-7glo + 1glox) = -1log(2) Reorder the terms: 1glo + -7glo + glox + 1glox = -1log(2) Combine like terms: 1glo + -7glo = -6glo -6glo + glox + 1glox = -1log(2) Combine like terms: glox + 1glox = 2glox -6glo + 2glox = -1log(2) Reorder the terms for easier multiplication: -6glo + 2glox = -1 * 2glo Multiply -1 * 2 -6glo + 2glox = -2glo Solving -6glo + 2glox = -2glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '2glo' to each side of the equation. -6glo + 2glo + 2glox = -2glo + 2glo Combine like terms: -6glo + 2glo = -4glo -4glo + 2glox = -2glo + 2glo Combine like terms: -2glo + 2glo = 0 -4glo + 2glox = 0 Factor out the Greatest Common Factor (GCF), '2glo'. 2glo(-2 + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Add '-1x' to each side of the equation. x + -1x = 2 + -1x Combine like terms: x + -1x = 0 0 = 2 + -1x Simplifying 0 = 2 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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